It's extremely rare for a false flag in the system to be overlooked and result in a legal program resulting in bans; every single ban wave (which can hit tens of thousands at once) tons of people will not understand the ban, so they band together and name off random programs they believe triggered it and latch onto something somewhat common between them. However, not only does that method of determining the false flag not hold any water, there are cheaters out there intentionally trying to cast doubt on the system and get out of bans they know they deserved.
Most of the time someone is banned for cheating and they know they didn't do so, it's because their account or computer was compromised and someone else had been using the program on their account or had it in their client. This includes playing on public computers where the player cannot control what's on the client.
If any player believes their ban to be an error, they should submit a ticket so player support can verify the ban. If they think or know their account was used by someone else at any point they should absolutely inform player support of the time frame for this.